Method and apparatus for instability compensation of V/Hz pulse width modulation inverter-fed induction motor drives

ABSTRACT

Index signals which represent the degree of instability in a three-phase induction motor system is derived by using phase current signals which are usually already available in V/Hz PWM inverters for other purposes. Proportional integration compensators, which may be implemented in software, process these index signals and generate frequency and/or voltage adjustments to the V/Hz controller in order to compensate for speed instability in the system. The compensation algorithm is robust to system changes and is also effective to improve acceleration and deceleration performance.

FIELD OF THE INVENTION

This invention relates generally to the field of induction motor drives,and more particularly to pulse width modulation inverters for inductionmotor drive systems.

BACKGROUND OF THE INVENTION

Using fast switching power semiconductor devices, such as insulated gatebipolar transistors (IGBTs), a pulse width modulation (PWM) inverter canbe operated at high frequency (up to 20 kHz), significantly improvinginduction motor performance. Advantages include lower electromagneticnoise, higher efficiency, and more output torque. Compared with speedfeedback-based current-regulated field orientation control, open loopvoltage/frequency ("V/Hz") control has the advantages of simplicity andcost effectiveness. Therefore V/Hz PWM inverter controls are widely usedin adjustable speed applications, such as fans, pumps, blowers, cranes,hoists, and so on. As more and more applications for V/Hz invertercontrols are discovered, more and more features are identified as beingdesirable, such as higher horsepower rating, quieter operation, higherefficiency, wider adjustable speed range, and wider load variationrange.

Under certain operation conditions, some problems with known voltageinverters have been perceived. One among these is an instabilityphenomena relating to the obvious and sustained speed oscillation ofmotors which can occur when they are driven by V/Hz PWM inverters.

Open loop V/Hz induction motor drives most often suffer instabilityproblems under light load and at low frequency. These problems canbecome even worse for large horsepower drives, high efficiency motors,and high PWM frequency operation, thus limiting the applications of suchdrives. The inventor and others have conducted extensive experimentalinvestigation to characterize such instability phenomena.

Instability problems with V/Hz inverters have been observed and analyzedby researchers. See, e.g.: Kunio Koga, "Stability Analysis andStabilizing Control of Inverter-Fed Induction Motor," ElectricalEngineering in Japan, Vol. 109, No. 3, pp. 130-140, 1989 ("Koga"); RyuzoUeda, Toshikatsu Sonoda and Shigeo Takata, "Experimental Results andTheir Simplified Analysis on Instability Problems in PWM InverterInduction Motor Drives," IEEE Trans. On Industry Applications, Vol. 25,No. 1, Jan./Feb. 1989, pp. 86-95 ("Ueda I"); Morris Lockwood,"Simulation of Unstable Oscillations in PWM Variable-Speed Drives," IEEETrans. On Industry Applications, Vol. 24, No. 1, Jan./Feb. 1989, pp.137-141 ("Lockwood"); Ryuzo Ueda, et al., "Stability Analysis inInduction Motor Driven by V/f Controlled General Purpose Inverter," IEEETrans. On Industry Applications, Vol. 28, No. 2, Mar./Apr., 1992, pp.472-481 ("Ueda II").

Stability analysis of induction motors fed by pure sinusoidal voltagemay be performed by using small signal linearization around theoperating point. See, e.g., P. C. Krause, O. Wasynczuk and A. D.Sudhoff, "Analysis of Electric Machinery," IEEE PRESS, 1994. For V/HzPWM inverter driven induction motors, the instability analysis becomesmore complicated. An idealized induction motor (IIM) has been proposedto analyze the effects of motor parameters, dead time and dc linkcapacitor. See, e.g., Koga. Later, these effects have also been analyzedbased on a practical induction motor model. See, e.g., Ueda II.Experimental investigations of the instability problem have beenconducted (see, e.g., Ueda I) in which an index was proposed to measurethe "degree of instability." System dynamic simulations have beenconducted to investigate these unstable oscillations. See., e.g.,Lockwood. These investigations and analyses have revealed some importantfacts about this problem. Some relevant points may be summarized asfollows:

(a) The oscillation states depend on motor design, such as motorparameters (resistance, inductance); the number of poles; motorgeometry; loss of core material; and the moment of rotor inertia.

(b) The oscillation states also depend on PWM inverter parameters suchas the dead time; dc link capacitor; PWM frequency and strategy.

(c) The oscillation states further depend on operating conditions suchas output frequency; shaft load, applied voltage and even the transitionpath to the operating point.

Those of ordinary skill in the art will generally understand that motoroscillations can result from uncontrolled energy exchanges among DC linkcapacitors, motor magnetic fields, and rotor inertia. Any mechanism todamp this energy exchange would be expected to stabilize theoscillation.

On the other hand, it can be difficult to derive an effectivestabilization control method, since many variables are involved in thephenomena. Koga has proposed a voltage vector feedback method to removethe effects of leakage inductance and primary resistance by using thephase current feedback. In Nobuyoshi Mutoh, et al., "Stabilizing ControlMethod for Suppressing Oscillations of Induction Motors Driven by PWMInverter," IEEE Trans. On Industrial Electronics, Vol. 37, No. 1, Feb.1990, pp. 48-56 ("Mutoh"), there is proposed a stabilizing controlmethod involving measuring the interval of negative and positiveinverter input currents. This requires a very precise circuit speciallydesigned for high PWM frequency. Recently, fuzzy inference algorithmshave been theoretically investigated for oscillation stabilization. See,e.g., Marek Budzisz, and Zbigniew Nowacki, "Stabilization ProceduresBased on Fuzzy Inference Algorithms for PWM Drives," Conference Recordof 1995 IAS Meeting, pp. 1663-1667 ("Budzisz").

An instability compensation method should preferably be effective,simple and robust. The investigated methods mentioned above are believedto have potential drawbacks, and the present invention is believed tooffer advantages over prior art methods and apparatuses.

SUMMARY OF THE INVENTION

Experimental investigation has been performed to characterize motorinstability phenomena. From these results, index signals which representthe degree of oscillation have been derived based on phase currentsignals which are usually already available in the V/Hz PWM inverter forother purposes. By processing these index signals, two decoupledproportional integration controllers, which may be implemented either inhardware or in software, are provided to generate command frequencyand/or voltage adjustment to a V/Hz controller.

In accordance with one aspect of the present invention, a compensationalgorithm and apparatus can be implemented in software and inserted intoexisting control code without any hardware modification. Therefore, thedisclosed method and apparatus is very simple and readily implemented.

In accordance with another aspect of the invention, the controlalgorithm is robust with respect to system changes. Also, the algorithmcan improve the acceleration and deceleration performance of drives.

BRIEF DESCRIPTION OF THE DRAWINGS

Various features and aspects of the present invention will perhaps bebest understood with reference to a detailed description of a specificembodiment of the invention, when read in conjunction with theaccompanying drawings, wherein:

FIG. 1 is a block diagram of a prior art PWM induction motor system;

FIG. 2 is a graph showing the waveform of two phase currents in thesystem of FIG. 1;

FIG. 3 is a graph showing the Fourier transform of the waveforms of FIG.2;

FIG. 4 is a graph showing the stator vector current in the system ofFIG. 1;

FIG. 5 is a graph showing the instability region of the system of FIG.1;

FIG. 6 is a block diagram of the instability compensation controller inaccordance with one embodiment of the invention;

FIG. 7 is an block diagram of a PWM induction motor system incorporatingthe instability compensation controller from FIG. 6;

FIG. 8 is a flow diagram illustrating the instability compensationmethodology employed in the system of FIG. 7; and

FIGS. 9a and 9b are graphs showing the effects of the instabilitycompensation controller on the phase currents and rotor speedoscillation in the system of FIG. 7.

DETAILED DESCRIPTION OF A SPECIFIC EMBODIMENT OF THE INVENTION

A block diagram of a prior art open-loop V/Hz PWM inverter-fed inductionmotor drive system 100 with which one embodiment of the invention mightbe used is shown in FIG. 1. In FIG. 1, system 100 is a 10 HP, 460 Vsystem where the inverter employs a third harmonic injected sinusoidalPWM scheme of adjustable carrier frequency from 2.5 kHz to 15.0 kHz andwith 3 μSec "dead time." (It is to be understood, of course, the presentinvention is in no way limited to systems having these particularspecifications, and those of ordinary skill in the art having thebenefit of the present disclosure will appreciate how the presentinvention may be practiced in a wide variety of contexts andapplications.)

As shown in FIG. 1, system 100 includes a source of three-phase AC power102, providing a three-phase AC power signal on three power supply lines104. In a customary and conventional arrangement, the AC power signal isapplied to diode bridge 106 for rectification into a DC signal presentedon DC bus lines 108 and 110. A capacitor 112 is disposed between buslines 108 and 110.

The DC signal on lines 108 and 110 is next applied to a power inverter114, which, in the presently disclosed embodiment of the invention is aninsulated-gate bipolar transistor (IGBT) inverter. As will be familiarand appreciated by those of ordinary skill in the art, inverter 114functions under control of a voltage/frequency (V/Hz) pulse widthmodulation (PWM) controller 116 to convert the DC signal on lines 108and 110 into a three-phase pulse-width modulation signal to be appliedto the windings of a three-phase induction motor 118.

As shown in FIG. 1, V/Hz PWM controller 116 receives voltage andfrequency reference signals which specify the desired voltage andfrequency of the PWM waveform to be generated. In one embodiment, anexternally-applied frequency reference signal is applied to V/Hzcontroller 116, as well as to a V/Hz profiler circuit 119. V/Hz profiler119 establishes a relationship between the frequency reference and thevoltage reference.

Pulse-width modulated motor control circuits are common andwell-understood. The details of the design and operation of such powercontrol electronics in controller 116 and inverter 114 are notconsidered relevant for the purposes of the present disclosure, andhence will not be discussed in depth herein.

As will be hereinafter described in further detail, the presentinvention may be advantageously employed in connection with the systemof FIG. 1, such that the motor currents are used as an indicator ofinstability based on their frequency spectrum.

Systems such as system 100 in FIG. 1 have been found to exhibitinstability problems at particular frequencies. For the system 100having the specifications discussed above, experimental data suggeststhat instability is likely to be most severe at an output frequency ofapproximately 20 Hz.

Current waveforms of two phases of motor 118 are shown in FIG. 2, andtheir corresponding fast Fourier transform (FFT) results, showing thefrequency spectra for the two phases, are given in FIG. 3. From FIG. 3it can be seen that the two currents have almost the same frequencycontent, and further that the major harmonics appear to be a side bandof the fundamental frequency. Also, there exist very strong half-ordersub harmonics, which can be expected to be a major contributor toundesirable speed oscillation.

The stator current vector locus is shown in FIG. 4. The trace in FIG. 4represents the stator current vector of motor 118 under sustainedoscillation. In FIG. 4, two major loops are evident, designatedgenerally with reference numerals 120 and 122. By varying either theoutput frequency or the output voltage from this worst point (i.e., 20Hz), instability can be gradually be reduced, as summarized in thefollowing Table 1.

                  TABLE 1    ______________________________________    INSTABILITY VS. OUTPUT FREQUENCY AND VOLTAGE                               MAJOR CURRENT    OUTPUT           FUNDA-    HARMONIC FREQUENCY    FREQU- OUTPUT    MENTAL    AND MAGNITUDE    ENCY   VOLTAGE   CURRENT   F.sub.-- h1                                     F.sub.-- h2                                          F.sub.-- h3                                               F.sub.-- h4    (Hz)   (V)       (A)       (Hz)  (Hz) (Hz) (Hz)    ______________________________________    20     339.0     9.40      1.10  0.84 40.6 0.92    20     269.5     3.88      11.2  1.12 28.9 1.12    20     315.5     6.36      10.0  3.39 30.0 3.82    18     315.5     8.40      1.10  0.68 36.6 0.92    22.5   315.5     5.00      10.7  0.82 34.3 0.88    ______________________________________

During this variation, the number of major loops in the stator currentvector (FIG. 4) increases, each of the loops moving gradually closeruntil the loops converge to appear as a single circle when stableoperation is achieved.

FIG. 5 illustrates the instability region of system 100 from FIG. 1. Inthe graph of FIG. 5, motor voltage is plotted along the vertical axisand output frequency is plotted along the horizontal axis. Theinstability region of the system at a 2.5 kHz PWM frequency isrepresented by the shaded area designated with reference numeral 124. Asthe PWM frequency is increased, the instability region increases. Theinstability region for the system at a 5.0 kHz PWM frequency isindicated by the dashed line designated generally with reference numeral126 in FIG. 5.

From the foregoing, some observations may been made: First, harmoniccontent is believed to be a good indicator of the instabilityphenomenon. Since there is no obvious and deterministic relationshipbetween these harmonics and the fundamental frequency, an open loopharmonic cancellation control seems unfeasible to design. Therefore, thepresent invention involves a feedback control method to compensate forcurrent harmonics associated with motor instability.

Second, given the instability region 124 as shown in FIG. 5, oneapproach to addressing problems with instability could be to adjust theoutput voltage out of the instability region. However, by doing so, themotor will not operate at the optimal design flux level. Further, thisapproach would not be expected to be as effective on high horsepowerdrives as on small drives, since high horsepower drives tend to exhibita wider instability region. Thus, in accordance with one aspect of theinvention, automatic compensation is achieved through a mechanism foridentifying the instability.

Identification of Instability

The purpose of instability identification in accordance with thepresently disclosed embodiment is to provide real-time signalsrepresenting degrees of instability. These signals are advantageouslyprovided to an instability compensator. In order to simplify the openloop V/Hz PWM control, the use of a speed feedback signal from theshaft-mounted speed sensor should preferably be avoided.

As those of ordinary skill in the art will be aware, in smaller controlsa DC bus current signal is commonly used for current protection, slipcompensation, status display, and the like. In larger V/Hz PWM controls,phase current sensing is usually employed for these purposes, since thedistributed DC bus structure makes bus current sensing difficult. Also,it has been proposed to use phase current sensing on smaller controls,since the bus current is a much noisier and less informative signal.Therefore, phase currents are preferably exploited to identifyinstabilities.

Using the concepts of space vectors (see, e.g., Peter Vas, ElectricMachines and Drives--A Space Vector Theory Approach, Oxford SciencePublications, 1992), the stator voltage balance equation of an inductionmotor can be expressed as: ##EQU1##

Where ν_(s) , i_(s) , and e_(m) are the stator voltage vector, thestator current vector, and back emf vector, respectively, and whereL.sub. s is the leakage inductance of the winding of motor 118. Thestator current vector i_(s) is calculated as: ##EQU2## where

    i.sub.α =-i.sub.b -i.sub.c                           (3)

and ##EQU3##

Under stable steady state operation, all vectors (voltage, current, andback emt) have fixed magnitude and rotate at a constant speed. Underunstable operation, the current vector has an oscillation in bothmagnitude and rotation speed, as discussed above. Therefore, the backemf vector can be expected also to oscillate in both magnitude androtation speed, since the voltage vector is tightly controlled by theV/Hz PWM controller to have fixed magnitude and rotation speed.

Considering that the back emf vector is associated with the rotor speedand air-gap flux, it has relatively slower dynamics than the currentvector. Therefore, the back emf vector can be assumed to be a constantduring a relatively short sampling period. Hence, Equation 1 abovesuggests a first order dynamic system with voltage vector as input,current vector as output and back emf as disturbance.

The oscillation of the current vector can be characterized by itsmagnitude change ##EQU4## and its angular speed change Δω, which can bemathematically expressed as follows: ##EQU5##

If the motor is running stably, both ##EQU6## and Δω should be zero.Thus, these two variables can be used to identify any instability. (Inone embodiment, the division operation in the calculation of Δθ (k) canbe discarded to save some execution time.)

Design of Compensation Controller

An instability compensation controller in accordance with the presentlydisclosed embodiment of the invention should preferably take the aboveinstability identifying signals ##EQU7## and Δω as its inputs. From themotor dynamics described by Equation 1 above, the output of thecompensation controller preferably should be the voltage vector Δν_(s) ,which is a two dimensional variable that can be decomposed to two scalarcomponents, such as Δ(ν.sub.α, ν.sub.β) in rectangular coordinates,##EQU8## in polar coordinates, or Δ(ν.sub.α, ν_(b), ν_(c) =-ν.sub.α-ν_(b)) in motor phase coordinates.

FIG. 6 is a simplified block diagram of an instability compensator 128in accordance with the presently disclosed embodiment of the invention.As shown in FIG. 6, instability compensator 128 comprises an instabilitydetector 130 and a proportional integration regulators 132. Inaccordance with one aspect of the presently disclosed embodiment of theinvention, instability detector 130 functions to compute the values##EQU9## and Δω (see Equations 5, 6, 7 and 8 above). These values arethe provided to proportional integration regulators 132, which use thesevalues to derive the incremental voltage vector Δν_(s) , as will behereinafter described in further detail.

To be compatible with a V/Hz PWM control 116 as shown in FIG. 1, thepolar decomposition of Δν_(s) may be employed. Considering that thecompensation controller is a kind of perturbation control superimposedonto the standard V/Hz PWM controller, its output needs to reflect thechanges of voltage magnitude and frequency. Therefore, proportionalintegration regulators 132 have a combined structure of two inputs andtwo outputs; as shown in FIG. 6, the inputs to regulators 132 are##EQU10## and Δω, while the outputs are ##EQU11## and ΔF.

A simple decoupled controller can be used to implement this proportionalintegration compensation algorithm according to the following equations:##EQU12##

Where K_(p)ν, K_(i)ν, K_(pf), and K_(if) are predetermined proportionalintegration coefficients which determine the characteristics ofproportional integration regulators 132 and hence determine compensationperformance. It is believed that those of ordinary skill in the arthaving the benefit of the present disclosure will be readily able toselect appropriate proportional integration coefficients depending uponvarious implementation-specific variables, such as desired compensationadjustment limits, compensation response, and so forth.

The incremental voltage angle is linearly related to the incrementalfrequency by the sampling period. That is, having computed ##EQU13## ΔFcan be computed by dividing Δ(∠ν_(s) ) by the sampling period.

As will be hereinafter described with reference to FIG. 7, the outputsof regulators 132 are respectively added to the voltage command andfrequency reference signals of a V/Hz controller 116 to provide theinstability compensation capability. Those of ordinary skill in the artwill appreciate that these proportional integration regulators 132 maybe readily implemented either in hardware or in software in a givenimplementation of the invention. When implemented in software, theproportional integration code can be inserted to the existing codewithout timing and task scheduling changes. Even a single frequencyadjustment can be effective for instability compensation.

Experimental investigations have shown that instability happens at loweroutput frequencies than the base frequency. The major oscillation isattributed to sub-harmonics, and the compensated frequency is usuallylow (4 Hz to 20 Hz). Therefore, the sampling frequency for the phasecurrent sensing is not critical, and about 1 kHz is enough. But sincethe differential is used, two phase currents have to be sampledsimultaneously. Otherwise, software compensation may be used to correctthe error from the sequential sampling.

To comply with signal noises, low pass filters at the input interim andoutput may be inserted in the digital signal processing. Also, limits onthe voltage and frequency adjustments may be made to take care ofextreme cases. In one embodiment, a 5 to 10% voltage limit and 0.5 Hz to2.5 Hz frequency limit are imposed. The time constant of the PIcontroller in the present embodiment is 4 mSec, and the gains aredetermined based on the current sensing scales and output limits.

FIG. 7 is an diagrammatic representation of system 700 in accordancewith the presently disclosed embodiment of the invention. To emphasizethe fact that the present invention may be advantageously employed inconnection with existing PWM drive systems, such as system 100 from FIG.1, elements of system 700 in FIG. 7 which are essentially identical tothose in system 100 in FIG. 1 have retained identical reference numeralsin FIG. 7,

As shown in FIG. 7, the system 700 receives the frequency referencesignal F₋₋ ref which specifies the desired frequency of the PWM waveformto be generated. F₋₋ ref is applied to V/Hz controller 116, as well asto V/Hz profiler 119 for derivation of the voltage reference signal V₋₋ref, in accordance with conventional practice in the art and asdiscussed above with reference to FIG. 1. Instability compensator 128samples two phases of the motor current, designated i_(b) and i_(c) inFIG. 7, to produce the ΔF and ΔV compensation signals discussed above.These compensation signals are summed with the F₋₋ ref and V₋₋ refsignals respectively, as represented by summation elements 134 and 136in FIG. 7, to achieve the instability compensation.

FIG. 8 is a flow chart illustrating the process of instabilitycompensation in accordance with the presently disclosed embodiment ofthe invention. From the starting point 140, the first step in thecompensation process is to sample two phases of the motor current, i_(b)and i_(c), as discussed above. This sampling is represented by block 142in FIG. 8. As will be appreciated by those of ordinary skill in the art,the sampling of the motor current is performed repeatedly duringoperation of motor system 100. In the disclosed embodiment, for example,the motor currents are sampled at a sampling rate of 1 kHz. Fornotational purposes, a given kth current sample pair {i_(b), i_(c) }will be designated herein as {i_(b) (k) and i_(c) (k)} while theimmediately preceeding current sample will be designated {i_(b) (k-1),i_(c) (k-1)}.

Next, i.sub.α and i.sub.β are calculated, in accordance with theEquations 3 and 4 above, as represented by block 144 in FIG. 8.

Each time i.sub.α and i.sub.β are calculated, these values are storedfor later use, as represented by block 146. That is, each time a pair{i.sub.α (k-1), i.sub.β (k-1)} is calculated, it is stored for laterderivation, in connection with a subsequent pair {i.sub.α (k), i.sub.β(k)}, of a "delta" or difference value, as will be hereinafterdescribed. Next, the current magnitude ##EQU14## is calculated,according to Equation 2 above, as represented by block 148. Each time##EQU15## is calculated, this value is stored, as represented by block150. That is, again, each time a value ##EQU16## is computed, it isstored for use, in connection with a subsequent value ##EQU17## toderive a difference value ##EQU18##

Also, as represented by block 152, the change of current angle Δθ iscalculated according to Equation 8 above. Each time Δθ is calculated,this value is stored for later use, as represented by block 154. Thatis, each time a value Δθ(k-1) is computed, it is stored for use with asubsequently computed value Δθ(k) in computing the "delta" or differencevalue Δω, according to Equation 8 above, as represented by block 158 inFIG. 8.

In block 156, the change in current magnitude, ##EQU19## is computed,using the value ##EQU20## calculated in block 148 and the previous value##EQU21## stored in block 150. Likewise, the change in current speed,Δω, is computed using the value Δθ(k) computed in block 152 and theprevious value Δθ(k-1) stored at block 154, according to Equation 7.

Having computed ##EQU22## and Δω, the compensation values ##EQU23## andΔF can now be derived, as represented by blocks 160 and 162,respectively.

In decision block 164, a determination is made whether the ##EQU24##voltage compensation value is larger than a predetermined upper limit.If not, the computed ##EQU25## is used as the voltage instabilitycompensation parameter to be summed with the voltage reference value V₋₋ref (see FIG. 7), as represented by voltage adjustment block 166 in FIG.8. If the computed ##EQU26## does exceed the predetermined limit, it isadjusted down to the limit, in block 168, and this adjusted value isused in adjustment block 166.

Similarly, in decision block 170, a determination is made whetherfrequency compensation parameter ΔF exceeds a predetermined limit. Ifnot, the computed value is used in frequency adjustment block 172.Otherwise, the ΔF parameter is adjusted down to the limit, in block 174,before compensation adjustment in block 172. This concludes thecompensation process (block 174).

As noted above, the present invention may be readily implemented andembodied in a software-based PWM motor controller, as would be apparentto anyone of ordinary skill in the art. Computer-based motorcontrollers, which operate under control of a PWM motor controllersoftware, are well known in the art. The following assembly-languagecode implements the instability compensation process in accordance withthe presently disclosed embodiment of the invention, as described abovewith reference to FIG. 8:

    ______________________________________    /* = =  =  =  =  =  =  = =  =  =  =  =  =  =function = =  =  =  =  =  =    = =  =  =  = */    void instability.sub.-- identification (void)    /* = = = = = = = = = = = = = = = = = = = = = = = = = = = = */    asm    {    ld       TR01, i.sub.-- ds;    shra     TR01, #5;    ld       TR45, Ialpha;    add      TR01, TR45;    shra     TR45, #2;    sub      TR01, TR45;                       /* TR01 = scaled Ialpha.sub.-- present */    ld       TR23, i.sub.-- qs;    shra     TR23, #5;    ld       TR45, Ibeta;    add      TR23, TR45;    shra     TR45, #2;    sub      TR23, TR45;                       /* TR23 = scaled Ibeta.sub.-- present */    }    /************************************************************     *   Calculation of Change of Angle                                       *    ************************************************************/    /* DAngle =    * Ialpha.sub.-- previous * Ibeta.sub.-- present - Ialpha.sub.-- present    *    Ibeta.sub.-- previous    */    asm mul TR4567,  TR23, Ialpha;    asm st  TR01,    Ialpha; /* update Ialpha */    asm ld  TR01,    Ibeta;    asm st  TR23,    Ibeta;    /* update Ibeta */    asm mul TR0123,  TR01, Ialpha;    asm sub TR45,    TR01;    asm subc            TR67,    TR23;     /* TR4567 = present DAngle */    asm ld  TR01,    DAngle.sub.-- 0;                               /* retrieve previous filtered    DAngle */    asm ld  TR23,    DAngle.sub.-- 1;    asm st  TR45,    DAngle.sub.-- 0;                               /* update filtered DAngle                                             */    asm st  TR67,    DAngle.sub.-- 1;    asm sub TR45,    TR01;     /* TR4567 =    */    asm subc            TR67,    TR23;     /* present DAngle - previous    DAngle */    /* Filter DAngle difference */    asm ld  TR01,    DAngle.sub.-- diff.sub.-- 0;    asm ld  TR23,    Dangle.sub.-- diff.sub.-- 1;    asm shral            TR0123,  #2;    asm shral            TR4567,  #2;    asm sub TR45,    TR01;    asm subc            TR67,    TR23;       asm add  TR45,    DAngle.sub.-- diff.sub.-- 0;                                   /* TR4567 =    */       asm addc TR67,    DAngle.sub.-- diff.sub.-- 1;                                   /* DAngle difference    filtered */    asm st  TR45,    DAngle.sub.-- diff.sub.-- 0;                                 /*update filtered    difference */    asm st  TR67,    DAngle.sub.-- diff.sub.-- 1;    asm SHLL            TR4567, #10;       /* TR67 = DAngle    Difference */    DAngle.sub.-- diff = TR67;    } /** instability.sub.-- identification( ) **/    /*= = = = = = = = = = = = = = = = = = = = =function = = = = = = = = = = =    7    void instability.sub.-- compensation (void)    /*= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =    {    if ( fx100.sub.-- diff |= 0 )                  /* Transient state, no stability    comp */    {    PIF.sub.-- int.sub.-- 0 >>= 2;    TR01 = fx100.sub.-- adj.sub.-- 0;    asm SHRA TR01, #1;    fx100.sub.-- adj = TR01;    fx100.sub.-- adj.sub.-- 0 = TR01;    }    else /* Steady state */    {    if ( final.sub.-- dir == FORWARD )    {    TR23 = DAngle.sub.-- diff;    }    else if ( final.sub.-- dir == REVERSE )    {    TR23 = -DAngle.sub.-- diff;    }    else    TR23 = 0;    fx100.sub.-- adj = TR23;                    /* Proportional control */    asm shra TR23, #1;    }    asm { SHRA TR23, #1;}                      /* Integral control */    PIF.sub.-- int.sub.-- 0 += TR23;    fx100.sub.-- adj += PIF.sub.-- int.sub.-- 0;    TR01 = freq.sub.-- limit;    if ( fx100.sub.-- adj > TR01 )    {    PIF.sub.-- int.sub.-- 0 = TR01;    fx100.sub.-- adj = TR01;    }    else if ( fx100.sub.-- adj < -(int)TR01 )    {    PIF.sub.-- int.sub.-- 0 = -(int)TR01;    fx100.sub.-- adj = -(int)TR01;    }    fx100.sub.-- adj.sub.-- 0 = fx100.sub.-- adj;    TR01 = fx100.sub.-- adj;    }    } /* instability.sub.-- compensation( ) */    ______________________________________

FIGS. 9a and 9b illustrate the beneficial effects of the instabilitycompensation system in accordance with the presently disclosedembodiment of the invention. FIG. 9a shows two phase currents i_(b) andi_(c), their waveforms being designated with reference numerals 180 and182 in FIG. 9a, and a waveform 184 representing the rotor speedoscillation. When instability compensation system 100 is activated, at atime represented by dashed line 186 in FIG. 9a, the phase currentsbecome almost sinusoidal and significantly less distorted. The speedoscillation essentially disappears. The transition following activationof system 100 takes approximately 500 mSec.

The experimental results represented in FIG. 9a reflect a system havinga 10 HP drive, a 20 Hz output, and 2.5 kHz PWM frequency. FIG. 9b, onthe other hand, presents corresponding experimental results from thesame system, except with a 8.0 kHz PWM frequency. The effects ofcompensation system 100 on dynamic performance (e.g., acceleration anddeceleration) have also be experimentally verified.

From the foregoing detailed description of a specific embodiment of theinvention, it should be apparent that a method and apparatus forinstability compensation in PWM induction motor systems has beendisclosed. Although a specific embodiment of the invention has beendescribed herein in some detail, it is to be understood that this hasbeen done merely to illustrate various features and aspects of theinvention, and is not intended to be limiting with respect to the scopeof the invention. It is believed that various substitutions,alterations, and/or modifications, including but not limited to thosedesign alternatives that may have been specifically mentioned herein,may be made to the disclosed embodiment of the invention withoutdeparting from the spirit and scope of the invention as defined in theclaims, which follow.

What is claimed is:
 1. A method of identifying instability in athree-phase induction motor drive system, comprising:(a) detecting, inan instability detector circuit coupled to at least two of three phasesof said motor drive system, a change ##EQU27## in the magnitude ofstator current in the system; and (b) detecting, in an instabilitydetector circuit coupled to at least two of three phases of said motordrive system, a change Δω in angular speed change in the system; and (c)identifying instability in said motor drive system based upon values of##EQU28## and Δω.
 2. A method in accordance with claim 1, wherein saidstep (a) of detecting a change ##EQU29## in the magnitude of statorcurrent in the system comprises: (c) sampling current in at least twophases of said system to obtain first current values i_(b) (k-1) andi_(c) (k-1);(d) susbsequently sampling in said at least two phases ofsaid system to obtain second current values i_(b) (k) and i_(c) (k); (e)computing ##EQU30## according to the formula ##EQU31## and where, forx=k and k-1,

    i.sub.α (x)=-i.sub.b (x)-i.sub.c (x)

and ##EQU32##
 3. A method in accordance with claim 2, wherein said step(b) of detecting a change Δω in angular speed change in the systemcomprises: (f) computing a value Δω according to the formula:

    Δω=Δθ(k)-Δθ(k-1)

where ##EQU33##
 4. A method of controlling a three-phase induction motordrive system, comprising: (a) detecting a change ##EQU34## in themagnitude of stator current in the system; (b) detecting a change Δω inangular speed change in the system;(c) computing a change Δν_(s) in avoltage vector ν_(s) derived from said change ##EQU35## in the magnitudeof stator current and said change Δω in angular speed change in saidsystem; and (d) adjusting said system's output based on said changeΔν_(s) in said voltage vector ν_(s) .
 5. A method in accordance withclaim 4, wherein step (a) of detecting a change ##EQU36## in themagnitude of stator current in the system comprises: (c) samplingcurrent in at least two phases of said system to obtain first currentvalues i_(b) (k-1) and i_(c) (k-1);(d) susbsequently sampling in said atleast two phases of said system to obtain second current values i_(b)(k) and i_(c) (k); (e) computing ##EQU37## according to the formula##EQU38## and where, for x=k and k-1,

    i.sub.α (x)=-i.sub.b (x)-i.sub.c (x)

and ##EQU39##
 6. A method in accordance with claim 5, wherein said step(b) of detecting a change Δω in angular speed in the system comprises:(f) computing a value Δω according to the formula:

    Δω=Δθ(k)-Δθ(k-1)

where ##EQU40##
 7. A method in accordance with claim 6, wherein saidstep (c) of computing a change Δν_(s) in said voltage vector ν_(s)comprises: (g) computing said change ##EQU41## according to theformulas: ##EQU42## where K_(p)ν, K_(i)ν, K_(pf), and K_(if) arepredetermined proportional integration constants.
 8. A method inaccordance with claim 7, further comprising:(h) adjusting a voltageparameter of said system in accordance with the magnitude ##EQU43## ofsaid change in said voltage vector ν_(s) .
 9. A method in accordancewith claim 8, further comprising:(i) adjusting a frequency parameter ofsaid system in accordance with a frequency compensation value ΔFcomputed according to the formula: ##EQU44## where sampling period is aconstant value corresponding to the time interval between said steps (c)and (d) of sampling at least two phases of current.
 10. An apparatus foridentifying instability in a three-phase induction motor drive system,comprising:instability detector circuitry coupled to at least two ofsaid three phases of said motor drive, for detecting a change ##EQU45##in the magnitude of stator current in the system and for detecting achange Δω in angular speed change in the system; and compensatorcircuitry coupled to said instability detection circuitry foridentifying instability based on values of ##EQU46## and Δω.
 11. Anapparatus in accordance with claim 10, wherein said instability detectorcircuitry samples said at least two phases of said system to obtainfirst current values i_(b) (k-1) and i_(c) (k-1) and subsequent secondcurrent values i_(b) (k) and i_(c) (k);processing circuitry forcomputing ##EQU47## according to the formula ##EQU48## and where, forx=k and k-1,

    i.sub.α (x)=-i.sub.b (x)-i.sub.c (x)

and ##EQU49##
 12. An apparatus in accordance with claim 11, wherein saidinstability detector circuitry comprises: circuitry for computing avalue Δω according to the formula:

    Δω=Δθ(k)-Δθ(k-1)

where ##EQU50##
 13. An apparatus for controlling a three-phase inductionmotor drive system, comprising: instability detector circuitry, coupledto at least two of said three phases of said motor drive, for detectinga change ##EQU51## in the magnitude of stator current in the system andfor detecting a change Δω in angular speed change in thesystem;processing circuitry for computing a change Δν_(s) in a voltagevector ν_(s) derived from said change ##EQU52## in the magnitude ofstator current and said change Δω in angular speed change in saidsystem; and control circuitry, responsive to said change ν_(s) in saidvoltage vector ν_(s) to adjust said system's output.
 14. An apparatus inaccordance with claim 13, wherein said instability detector circuitrycomprises:a sampling circuit for sampling current in at least two phasesof said system to obtain first current values i_(b) (k-1) and i_(c)(k-1) and subsequent second current values i_(b) (k) and i_(c) (k); andprocessing circuitry for computing ##EQU53## according to the formula##EQU54## and where, for x=k and k-1,

    i.sub.α (x)=-i.sub.b (x)-i.sub.c (x)

and ##EQU55##
 15. An apparatus in accordance with claim 14, wherein saidinstability detector circuitry comprises: circuitry for computing avalue Δω according to the formula:

    Δω=Δθ(k)-Δθ(k-1)

where ##EQU56##
 16. An apparatus in accordance with claim 15, whereinsaid processing circuitry for computing a change Δν_(s) in said voltagevector ν_(s) comprises: circuitry for computing said change ##EQU57##according to the formulas: ##EQU58## where K_(p)ν, K_(i)ν, K_(pf), andK_(if) are predetermined proportional integration constants.
 17. Anapparatus in accordance with claim 16, further comprising: voltagecontrol circuitry responsive the magnitude ##EQU59## of said change insaid voltage vector ν_(s) to adjust a voltage parameter of said system.18. An apparatus in accordance with claim 17, furthercomprising:frequency control circuitry responsive to a frequencycompensation value ΔF to adjust a frequency parameter of said system,wherein said frequency compensation value ΔF is computed according tothe formula: ##EQU60## where sampling period is a constant valuecorresponding to the time interval between said steps (c) and (d) ofsampling at least two phases of current.